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The PI Property in Algebras of Polynomial Type

James Gómez, Claudia Gallego

Abstract

This article provides a synthesis of recent advances in the study of the PI property in various classes of noncommutative algebras of polynomial type.

The PI Property in Algebras of Polynomial Type

Abstract

This article provides a synthesis of recent advances in the study of the PI property in various classes of noncommutative algebras of polynomial type.
Paper Structure (9 sections, 38 theorems, 210 equations)

This paper contains 9 sections, 38 theorems, 210 equations.

Table of Contents

  1. Introduction
  2. Double Ore extensions
  3. Two-parameter quantum Heisenberg algebra
  4. Quantum Matrix Algebra
  5. The algebra Uq+
  6. Quantized Weyl Algebras
  7. Bi-quadratic algebras on 3 generators
  8. Down-Up algebras
  9. Álgebra Bq(f)

Key Result

Lemma 2.4

Let $B = A_P[x_1,x_2;\sigma, \delta, \tau]$ be a right double Ore extension of $A$, with $\{ \sigma,\delta \}$ those morphisms determined by (R2). The following holds

Theorems & Definitions (82)

  • Remark 1.1
  • Definition 2.1: Zhang
  • Definition 2.2
  • Lemma 2.4: Zhang
  • Example 2.5
  • Example 2.6
  • Example 2.7: Zhang
  • Theorem 2.8: Zhang
  • proof
  • Remark 3.1
  • ...and 72 more